# Program to find total number of edges in a Complete Graph

Given N number of vertices of a Graph. The task is to find the total number of edges possible in a *complete graph* of N vertices.**Complete Graph:** A Complete Graph is a graph in which every pair of vertices is connected by an edge. **Examples**:

Input : N = 3 Output : Edges = 3 Input : N = 5 Output : Edges = 10

The total number of possible edges in a complete graph of N vertices can be given as,

Total number of edges in a complete graph of N vertices= ( n * ( n – 1 ) ) / 2

**Example 1:** Below is a complete graph with N = 5 vertices.

The total number of edges in the above complete graph = 10 = (5)*(5-1)/2.

Below is the implementation of the above idea:

## C++

`// C++ implementation to find the` `// number of edges in a complete graph` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the total number of` `// edges in a complete graph with N vertices` `int` `totEdge(` `int` `n)` `{` ` ` `int` `result = 0;` ` ` `result = (n * (n - 1)) / 2;` ` ` `return` `result;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 6;` ` ` `cout << totEdge(n);` ` ` `return` `0;` `}` |

## Java

`// Java implementation to find the` `// number of edges in a complete graph` `class` `GFG {` ` ` `// Function to find the total number of` `// edges in a complete graph with N vertices` `static` `int` `totEdge(` `int` `n)` `{` ` ` `int` `result = ` `0` `;` ` ` `result = (n * (n - ` `1` `)) / ` `2` `;` ` ` `return` `result;` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `main(String []args)` ` ` `{` ` ` `int` `n = ` `6` `;` ` ` `System.out.println(totEdge(n));` ` ` `}` `}` |

## Python 3

`# Python 3 implementation to ` `# find the number of edges` `# in a complete graph` `# Function to find the total` `# number of edges in a complete` `# graph with N vertices` `def` `totEdge(n) :` ` ` `result ` `=` `(n ` `*` `(n ` `-` `1` `)) ` `/` `/` `2` ` ` `return` `result` ` ` `# Driver Code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `n ` `=` `6` ` ` `print` `(totEdge(n))` `# This code is contributed` `# by ANKITRAI1` |

## C#

`// C# implementation to find` `// the number of edges in a` `// complete graph` `using` `System;` `class` `GFG` `{` ` ` `// Function to find the total` `// number of edges in a complete` `// graph with N vertices` `static` `int` `totEdge(` `int` `n)` `{` ` ` `int` `result = 0;` ` ` `result = (n * (n - 1)) / 2;` ` ` `return` `result;` `}` `// Driver Code` `public` `static` `void` `Main()` `{` ` ` `int` `n = 6;` ` ` `Console.Write(totEdge(n));` `}` `}` `// This code is contributed` `// by ChitraNayal` |

## PHP

`<?php` `// PHP implementation to find` `// the number of edges in a` `// complete graph` `// Function to find the total` `// number of edges in a complete` `// graph with N vertices` `function` `totEdge(` `$n` `)` `{` ` ` `$result` `= 0;` ` ` `$result` `= (` `$n` `* (` `$n` `- 1)) / 2;` ` ` `return` `$result` `;` `}` `// Driver Code` `$n` `= 6;` `echo` `totEdge(` `$n` `);` `// This code is contributed` `// by Shivi_Aggarwal` `?>` |

## Javascript

`<script>` `// Javascript implementation to find the` `// number of edges in a complete graph` `// Function to find the total number of` `// edges in a complete graph with N vertices` `function` `totEdge(n)` `{` ` ` `var` `result = 0;` ` ` `result = (n * (n - 1)) / 2;` ` ` `return` `result;` `}` `// Driver Code` `var` `n = 6;` `document.write( totEdge(n));` `</script>` |

**Output:**

15

**Time Complexity:** O(1)**Auxiliary Space:** O(1)